True, but not if you've gone through more than 10 years in school being taught to panic if you see the % sign, which was what today's teachers did when they went to school.

True stories from our schools include the little boy who was asked what 6 times 9 is and immediately replied 54 explaining that 5×10 is 60, so 6×9 must be 60-6=54. The teacher was not happy at all since the reply meant that the boy hadn't memorised the multiplication table.

I've heard a story about our great mathematician Niels Henrik Abel. When a little boy at school his teacher asked the pupils to sum all the numbers from 1 to 100 thinking that it would keep them busy for a while. But Niels Henrik quickly replied 5050 explaining that since 1+100=101, 2+99=101 and so on until 50+51, the answer must be 50*101 = 5050. His talent for math was discovered early, but in today's school teachers would not approve an answer like that, but rather requirie the pupil to show the calculation and intermediate steps for 1+2+3+...

but in today's school teachers would not approve an answer like that, but rather requirie the pupil to show the calculation and intermediate steps for 1+2+3+...

Yes, I did poorly in many math classes because I understood how to solve the problems, but just figured it out in my head rather than showing all the steps (or worse, in geometry, knowing the names of all those pointless theorems when doing proofs).

Yes, I did poorly in many math classes because I understood how to solve the problems, but just figured it out in my head rather than showing all the steps (or worse, in geometry, knowing the names of all those pointless theorems when doing proofs).

I had geometry last year, so I understand your plight. Many intermediate steps are not worth putting on paper (especially proofs, I shouldn't have to use "something is equal to itself" to prove anything, that is common sense), but you lose points for arriving at the correct answer but not showing every thought that went through your head.

you lose points for arriving at the correct answer but not showing every thought that went through your head.

That's fine, to a reasonable level of detail.

I gradually began skipping math homework and the teacher didn't bother as long as did well on tests. I sometimes slept or did other things in class. I rarely read the books, and my philosophy was that I would make it through the curriculum and get sufficient experience with exercises by doing the exams. So I didn't bother to pay attention in classes anything more than required to understand the questions in exercises, while figuring out how to solve it I would do at the exam. But that made me pretty unprepared for university. I'm not particularly gifted in math. I only get math intuitively or quickly up to a certain level, and that apparently roughly corresponded to anything up to but not including university level. I wish now I had got more challenges in school.

I only get math intuitively or quickly up to a certain level, and that apparently roughly corresponded to anything up to but not including university level.

I was the same way. Any kind of math I took before calculus I got easily. But calculus I couldn't get intuitively, at least beyond the easiest parts of it. What I don't understand is why it's a required course at universities. When are you ever going to need to know calculus? It's only applicable to a narrow range of job specializations. If you're planning on becoming a history or language major then it's a waste of time, and it could serve to keep an otherwise very qualified person out of their career if completing calculus courses is a graduation requirement. This is one problem I have with the system of education we have.

HarbingerDawn, my grandfather was a director of "physical-mathematical lyceum", that is, by definition, an analogue of college with deeper studying of these disciplines. IMHO(but not exclusively mine) mathematic is a very important part of education. They say, "math is the Queen of the Sciences", or "only by the math it is determined how much of science in the discipline", and finally, the byword "mathematics is useful at least because it puts your mind in order".

That is, if you can't grasp the level of math above the average or intuitive, you are no trying much, you're not devoted to education, you're loosing the part of your future life.

Quote (HarbingerDawn)

What I don't understand is why it's a required course at universities. When are you ever going to need to know calculus? It's only applicable to a narrow range of job specializations. If you're planning on becoming a history or language major then it's a waste of time

Statistics? Processing of research results? Application issues? This is not a problem. The laziness of your mind is a problem.

You can say it about any other discipline, language, history, economics, even physics, it all can be corrected if you know "how to do the math", but if you don't know math, this can't be corrected(at least without exceptional effort). I heartily thankful to my teachers that they brought me tho this understanding.

What I don't understand is why it's a required course at universities.

An introduction is always a good thing. Math in general, and certainly calculus, is a toolbox. No, hardly anyone has the need to use calculus regularly. And most will forget most of what they learn in calculus (I certainly have, and it's more than 20 years ago). But that is fine. What should stick is the ability to recognise what tool to use for a problem when you face it. If it can be solved using integrals, you would hardly guess it unless you've had some calculus. It's not important if you've forgotten it, since you then know where to look it up.

Another aspect of learning stuff that you might not really need is that it could lead to new insight. For instance, why does this weird constant e appear so many places in math? Or how come that you can use imaginary numbers for real world problems? Or is it not handy to know how abstract ideas can have a way to describe them in math and a way to reason about them (not calculus, but multidimensional stuff, for instance). Such insight might make the course worthwhile, though it will have no direct and immediate application.

Such insight might make the course worthwhile, though it will have no direct and immediate application.

I agree with this. I just think that it makes no sense to bar someone from pursuing their career of choice if they have trouble with calculus, because that effectively mandates that everyone has to be competent in it before they can proceed in life. I have a problem with that. Society places too much emphasis on grades and test results and "qualifications" (i.e. degrees) and seems to care little for what individuals are actually capable of. Some people are extraordinarily capable, but have specific weaknesses that make them bad at advancing through the school system. The way society is structured today, those people would never be able to achieve what they should, and their lives would be ruined. The only exception is if some of those people also have exceptional entrepreneurial skill and can thus forge their own path in life through business. Or maybe unless they're extremely lucky and meet some rare circumstance that will allow them to progress in life as they should. But these are not things that we should depend upon for people to live fulfilling lives and meet their potential. And to make matters worse, in my country a university education is very expensive, and for most people it is impossible to get without going into debt. This is another effective mandate in society: you cannot proceed in life unless you are wealthy, or unless you are willing to put yourself into a level of debt that you might possibly never be able to repay. Something has to change.

Sorry for the lack of paragraphs, I could just find no place for them in my rant.

Aerospacefag, I don't deny that a math education is very important. Maybe you did not understand what I was saying. I was saying that if someone cannot grasp some part of calculus, that should not prevent them from proceeding in life. It should only prevent them from doing things in which calculus might be applicable. But if they want to become a historian or a writer or a linguist, then what does it matter if they know how to find the area under a curve? You are preventing skilled people from using their skills to better society simply because their skills do not include some specific concepts in higher math, which are irrelevant to the jobs they would have anyway. It is disgraceful.

And to make matters worse, in my country a university education is very expensive, and for most people it is impossible to get without going into debt.

I think it's unrealistic to think that one should be able to finish university with no debt. In my country the university is totally free, but housing and food is not, and though there are some grants to be had, it will only cover a fraction of a very modest living. I began at the university with about $3000 (what I got after one year in military service), half of which or more I spent on buying a PC, and 8 years later I graduated, also having worked (about three years effectively if summing up part time) with about $30,000 in debt. Which I believe is not bad. Economically education is often an investment. In the long run it ought to pay off. But as with any investment, it's not risk free. If it was no economical risk, I think the paycheck differences would be smaller as well, and an incentive for getting educated people would disappear.

I totally agree that people have equal chances to go to university, but I don't think it should be risk free.

I agree with what was said here. More than finding a solution, teachers just want you to reproduce what they have learnt to you. It's particularly true in France. That's not surprising.

Teachers don't have time to check every students. So they just want to know if you understood what they said previously, if you are able to reproduce a method. People who are thinking differently are always a problem. School is for the mass. School is here to make sure that 80% of the people will understand, or, at least, will be able to reproduce a process. If you are in the 10% of the upper class (or, of the "2%" gifted students) you will probably have some difficulties...

It's only after many (MANY) years that a sort of "personal thinking" is valued.

I had once a bad mark in maths, because I named the unknowns differently from what was expected...

If you are in the 10% of the upper class (or, of the "2%" gifted students) you will probably have some difficulties...

This seems like a cop out to me. Just because one is gifted doesn't mean they will have trouble and just because someone has trouble doesn't mean that they are gifted.

If you cannot function by what society has deemed necessary then the fault is not on society but on you. I am not saying that our education system is perfect, nor am I supporting it. However our current system works for the large majority and that is what matters.